A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R round the same planet will have a period (in hours)

A satellite in a circular orbit of radius R has an orbital period of 4 hours. For another satellite orbiting the same planet with a radius of 3R, its orbital period can be determined using Kepler’s law of periods. The ratio of the orbital periods is proportional to the ratio of their orbital radii raised to the power of three-halves. Substituting the values, the period ratio is (3 R/R)³/² = √27. Therefore, the period of the second satellite is √27 x 4, or approximately 4√27 hours.

T₂/T₁ = (3 R/R)³/² = √27
T₂ = √27T₁ = 4√27 h.